A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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Diagonal stress energy tensor components

If I got a diagonal stress energy tensor $T_{\alpha \alpha} = x_{\alpha}$ for some coefficients $x_{\alpha}$, could anyone tell me how can I extract the four components of the stress energy tensor. ...
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142 views

Is the equivalence principle in General Relativity an approximation?

I read in web that Einstein used the principle of equivalence to explain General Relativity but we know the gravitation is approximately equal in all of rested frame in gravitional field. In ...
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Present experimental status of Moffat's Modified theory of Gravity

Modified theories of Gravity have been discussed before in this 2-year old question, Are modified theories of gravity credible? I was going through Moffat's modified gravity, given in ...
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265 views

Transformation rule of a partial derivative

We know the following transformation rule: $$ \partial'_b = \frac{\partial}{\partial x'^b} = \frac{\partial x^c}{\partial x'^b} \, \frac{\partial}{\partial x^c} = \frac{\partial x^c}{\partial x'^b} ...
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224 views

Why is there a gravitational attraction between two objects at rest with respect to each other?

From my understanding of relativity, gravity is not a force, but a result of the curvature of spacetime. If Object1 moves past Object2, even though it's moving in a straight line, its direction may ...
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318 views

Schwarzschild solution in arbitrary dimensions

Is there any generalized Schwarzschild solution for an arbitrary number of dimensions? Is it necessary to calculate each individually, or is there a relationship between them?
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What's the relation between the Euler $\psi$ function, the digamma function, and the hypergeometric function?

Can somebody help me out with the intermediate details of eqn. (2.5) in this paper? Generalized gravitational entropy. Aitor Lewkowycz and Juan Maldacena. arXiv:1304.4926. Is the Euler $\psi$ ...
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395 views

Can a scalar field model gravity? How accurate would be the results? Are there any difficulties with such a model?

Newtonian gravity can be described by the equation: $$ \nabla^2 \phi = 4 \pi \rho G $$ where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational ...
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272 views

Does the concept of a wormhole violate the law of mass-energy conservation?

If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space ...
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548 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
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Coordinate transformations of the metric tensor

Let's have metric (it describes the space-time of uniformly accelerating observer in Minkowski space-time) $$ ds^2 = v^2du^2 - dv^2. \qquad (.0) $$ I need to find expressions for $u = f(x, t), v = ...
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Can matter really fall through an event horizon?

This question is closely related to Event horizons without singularities from about a year ago (May 2012), which John Rennie answered nicely and persuasively. My variant of the question is this: ...
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835 views

Covariant and contravariant vectors

Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8)) The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in ...
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359 views

Check it the Killing vectors satisfy Killing equation or not

I am going through Kerr/CFT correspondence paper again, and I am at the section where authors specify Killing vectors for near horizon extreme Kerr metric (shortly NHEK). The metric is ...
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1k views

Why gravity is an attractive force? [duplicate]

Why gravity is an attractive force? One may say that it is because of space time curvature but General Relativity is built on this law: $\displaystyle G \frac{m_1 \times m_2}{r^2}$ (To be more ...
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112 views

Whose reference frame to use for $d \theta$ near a black hole?

Using the Schwarzchild metric for a body circularly orbiting a nonspinning black hole (i.e. $dr=0$), the relation between $d\tau$, the time between two light pulses sent out infinitesimally close ...
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134 views

General Relativity and Time Dilation [duplicate]

Is time affected by the gravitational force? If so, what might be the effect on time at the centre or near centre of earth ?
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256 views

Raising indices in Killing equation or not?

I'm having issues with computation of Killing equation. I'm using Mathematica to check if the given vectors are Killing vectors or not, and by hand for simple vector like $\xi=\partial_t$ I get the ...
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383 views

Is it true to say *Space time curvature* $\Leftrightarrow$ *Matter*

Is it true to say Space time curvature and Matter are just the same thing, part of the same coin and that therefore Space time curvature $\Leftrightarrow$ Matter? In other words is Space time ...
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Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other ...
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674 views

Parallel Transport of a 4-vector

Why does the parallel transported $4$-vector change from $X^a(x)$ to $X^a(x) + \bar{\delta}X^a(x)$ ? This is also discussed in D'Inverno's relativity book [page - 72]; but the reason is not clear.
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131 views

On Einstein's equivalence principles

There are two foundative Equivalence Principles in General relativity: Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and ...
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407 views

Weight of a tensor density

Is there any freedom in choosing the weight of a tensor density? I have seen in some papers that they introduce a tensor density made from metric with a special weight. There is a tensor density with ...
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Is it possible that a matter field has a dependent on non-radial space-like coordinate in a spacetime with spherical symmetry?

After the work from Breitenlohner and Freedman, we know matter fields in asymptotically AdS spacetime can be stable out of the black hole under some special conditions. My question: In such a ...
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Is a QFT in a classical curved spacetime background a self-consistent theory?

EDIT: Better rewording by Chris White: Is it possible to have a theory that treats both GR and QFT (e.g. QFT on a curved spacetime dynamically influenced by the standard QFT fields)? Is such a theory ...
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352 views

Showing that the variation of an affine connection is a tensor

How can i show that $\delta\Gamma_{\mu\nu}^{\rho}$ transforms like a tensor? Metric compatibility is not assumed here. That means 1) First i need to compute $\delta\Gamma$ first. To do that i need ...
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In relativity, can/should every measurement be reduced to measuring a scalar?

Different authors seem to attach different levels of importance to keeping track of the exact tensor valences of various physical quantities. In the strict-Catholic-school-nun camp, we have Burke ...
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'Easy way' of finding out the Killing vector fields?

Is there a way for calculating the Killing vector fields of a given metric in a quick way? Sure I can guess looking at the metric at the symmetries, and then guess some of them, but, for instance, in ...
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453 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
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486 views

Naive quantum gravity

My question involves an analogy I have to point out. Consider the Lagrangian density for the a complex scalar field: \begin{equation} ...
2
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2answers
138 views

Distinguish between Past and Future

When writing the metric in Minkowski space, how can we distinguish between the past and the future? I understand the answer after drawing the light cone but I want to know how we get that by just ...
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1answer
3k views

Riemann tensor in 2d and 3d

Ok so I seem to be missing something here. I know that the number of independent coefficients of the Riemann tensor is $\frac{1}{12} n^2 (n^2-1)$, which means in 2d it's 1 (i.e. Riemann tensor given ...
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739 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
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Schwarzschild metric in a different coordinate system

In PADMANABHAN, Gravitation (Foundations and Frontiers), Cambridge, p $304$, exercice $7.6$, an example of the Schwarzschild metric in a different coordinate system is given : $$\mbox{d}s^2= ...
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Geodesic in general relativity aproaching ellipse

In the gravity well-like 2d surfaces that are used in documentaries to illustrate the fact Earth orbits the Sun, I don't seem to find any kind of geodesic that will at least resemble an ellipse... ...
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191 views

Quantization surface in QFT

What does the Quantization Surface mean here? Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization
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80 views

Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
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Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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414 views

Asymmetric Schwarzschild solution - unequal mass on each side

Look at any Kruskal–Szekeres coordinate plot of the Schwarzschild solution. It shows the same mass everywhere. Yet the two sides cannot talk to each other, in that no information, particles, etc can ...
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358 views

Is spacetime all that exists?

Someone claiming to have studied physics is telling me that spacetime is all that exists and that this fact is the basis of modern physics. When I said matter/energy also exists in its various forms, ...
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1answer
192 views

Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...
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2answers
604 views

Speed of light in a gravitational field ?

How do I solve the speed of light in gravitational field? Should I just add gravitational acceleration in speed of light? $c'=c_0+g(r)t$?
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2answers
247 views

Does the total mass of an isolated object include the mass stored in its gravitational field?

Since neither the object nor its field could exist without the other, it would seem strange not to include the field energy as part of the object. But how exactly does the accounting go? How is the ...
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102 views

Relativity question: frequency shift under constant acceleration

Okay, my buddy tells me this: Let there be a starship, ovoid, and me and my buddy stand each at the extremities of the ship, him below the roof, me on the floor. We start a journey and the ship ...
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Finding superpotentials and central charges in $AdS_3$

In text "Covariant theory of asymptotic symmetries, conservation laws and central charges" is given an example of finding central charges and superpotential (among other things). I am interested in ...
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148 views

Does Hawking radiation break asymptotic flatness?

Basically what the question says -- there is reason to expect that, if allowed to continue long enough for the radiation to reach future null infinity, the fact that the radiation will fall off at ...
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Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: The effects of Wheeler's quantum foam on black hole growth are explored from an ...
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117 views

How does the warping of time behave as a fourth dimension?

My problem is that I have a hard time grasping something if I can't conceptualize it, though maybe this can not be conceptualized, just accepted, in which case I thank you for your patience. The ...
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Expansion of the universe and strain

From cosmological models that involve expansion of the universe, can we not say that there are ever increasing tidal forces felt by solid bodies? If so, the material in solid bodies like metal ...
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What is the mass in $\vec{\nabla}\cdot \vec{B}_g=\text{something}$ called if it could be non-zero?

Maxwell's equation for gravity has $$\vec{\nabla}\cdot \vec{B}_g~=~0,$$ see Gravitoelectromagnetism in analogy with the electrodynamics. What is the mass called that needs to make these equations ...